Contradiction with Numbers 16:40
Exodus 28:29 prescribes a specific priestly practice for remembrance, whereas Numbers 16:40 emphasizes that only Aaron's descendants should approach to offer incense, indirectly limiting priestly actions.
Numbers 16:40: [To be] a memorial unto the children of Israel, that no stranger, which [is] not of the seed of Aaron, come near to offer incense before the LORD; that he be not as Korah, and as his company: as the LORD said to him by the hand of Moses.
Contradiction with Hebrews 7:12
Exodus 28:29 describes the continuity of priestly tradition through Aaron, but Hebrews 7:12 argues for a change in the priesthood, and consequently, a change in the law.
Hebrews 7:12: For the priesthood being changed, there is made of necessity a change also of the law.
Contradiction with Jeremiah 31:34
Exodus 28:29 emphasizes the role of a priest as an intercessor before God, whereas Jeremiah 31:34 indicates no need for intercession as people will directly know God.
Jeremiah 31:34: And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Contradiction with Galatians 3:28
Exodus 28:29 distinguishes the duties and identity of the tribal priests, while Galatians 3:28 suggests that all distinctions, including those of tribe, are abolished in Christ.
Galatians 3:28: There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.
Contradiction with 1 Peter 2:9
Exodus 28:29 contacts priestly functions for the tribe of Levi, but 1 Peter 2:9 expands priestly status to all believers as a royal priesthood.
1 Peter 2:9: But ye [are] a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light: [peculiar: or, purchased] [praises: or, virtues]
Paradox #1
The potential contradiction in Exodus 28:29 might relate to the idea of intercession by priests, as it describes the high priest bearing the names of the tribes of Israel before God. Some might see a conflict with the belief that Jesus is the sole mediator between God and humans, as stated in the New Testament, thereby raising questions about the role of other mediators.
Paradox #2
The moral conflict with Exodus 28:29 could arise from the idea that it places emphasis on ritualistic and symbolic acts carried out by a specific person (the high priest) to represent the people before God. Some may see this as inconsistent with the belief that everyone can communicate with God directly, without needing an intermediary. This could contrast with the idea of personal and individual relationships with God, as emphasized in other parts of the Bible.